Heat transfer at the nanoscale : The hyperbolic heat equation

Abstract

The interest of taking technology to increasingly small scales has required great changes and advances in science. In particular, the well-known Fourier's law (very useful in large scales) has proved to be not accurate enough for describing heat transfer at smaller scales. The goal of this work is to introduce one of the alternatives to Fourier's law, the Cattaneo-Vernotte equation, and the resulting heat transfer model, the Hyperbolic Heat Equation. Numerical and analytical solutions will be provided and two case studies will be analysed, particularly studying the limit between the Parabolic and Hyperbolic Heat Equations at the nano and microscale.